\[ \text{T1D | Metabolite} \sim \text{Bern}(\text{logit}(\alpha_0 + \alpha_1*\text{Metabolite}))\\ \text{Methylation | Metabolite, T1D} \sim \text{N}(\delta+\gamma*\text{Metabolite}+\beta*\text{T1D},\sigma^2)\\ \]
\[ \alpha_0 \sim \text{N}(0,100)\\ \alpha_1 \sim \text{N}(0,100)\\ \delta \sim \text{N}(0,100)\\ \gamma \sim \text{N}(0,100)\\ \beta \sim \text{N}(0,100)\\ \sigma^2 = \frac{1}{\tau}\\ \tau \sim \text{Gamma}(0.0001,0.0001) \]